ΔE 15.2, loose: different enough that you should pick on purpose. Light Rust is noticeably darker, more saturated, cooler than Earth Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Light Rust is noticeably darker, more saturated, cooler than Earth Brown.
The same difference applies the other way round: Earth Brown is noticeably lighter, more muted, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Earth Brown on the colour wheel See Light Rust on the colour wheel
All matches: Earth Brown equivalents · Light Rust equivalents